Quark matter: the high-density frontier Mark Alford Washington - - PowerPoint PPT Presentation

Quark matter: the high-density frontier

Mark Alford Washington University in St. Louis

Outline

I Quarks at high density Confined, quark-gluon plasma, color superconducting II Color superconducting phases Color-flavor locking (CFL), and beyond III Quark matter in the real world Battle between color superconductivity and the strange quark mass IV Quark matter in neutron stars Mass-radius: signatures of a first-order transition Mergers: the role of transport and dissipation V Looking to the future

• I. Quarks at high density

Conjectured QCD phase diagram

superconducting quark matter = color− liq

T µ

gas

QGP CFL

nuclear /supercond superfluid

compact star

non−CFL

heavy ion collider

hadronic

heavy ion collisions: crossover and chiral critical point [ Stephanov (Mon) ] compact stars: color superconducting quark matter core?

Color superconductivity

BCS pairing mechanism

p E

µ

applies to degenerate fermions with an attractive interaction:

• electrons in a cold metal
• 3He atoms
• neutrons in nuclear matter
• quarks in quark matter

|BCS =

• p>pF

particles

• cos(θp)+sin(θp)a†

pa† −p

p<pF holes

• cos(θp)+sin(θp)apa−p
• Fermi

sea

• |BCS, not |Fermi sea, is the ground state.

Physical consequences of Cooper pairing

Changes low energy excitations, affecting transport properties.

◮ Goldstone bosons: massless degrees of freedom arising from

spontaneous breaking of global symmetries. Dominate low energy behavior, e.g.: Superfluidity

◮ Meissner effect: exclusion of magnetic fields arising from

spontaneous breaking of local (gauged) symmetries. Massive gauge bosons, e.g.: Superconductivity

◮ Gap in fermion spectrum.

Adding a fermion near the Fermi surface now costs energy because it disrupts the condensate. a†

p(cos θ + sin θ a† pa† −p) = cos θ a† p

Fermions frozen out of transport

E p ∆

particle hole qua s i h

• l

e qua r t p a icle si

Handling QCD at high density

Lattice: “Sign problem”—negative probabilities [ Bedaque (Mon) ] Holography: gravity dual of QCD-like theory [ Mateos (Mon) ] large N: Quarkyonic phase? pert: Applicable far beyond nuclear density. Neglects confinement and instantons. NJL: Model, applicable at low density. Follows from instanton liquid model. EFT: Effective field theory for lightest degrees of freedom. “Parameterization of our ignorance”: assume a phase, guess coefficients of interaction terms (or match to pert theory),

• btain phenomenology.

• II. Color superconducting phases

Attractive QCD interaction ⇒ Cooper pairing of quarks. We expect pairing between different flavors . Quark Cooper pair: qα

iaqβ jb

color α, β = r, g, b flavor i, j = u, d, s spin a, b =↑, ↓

Each possible BCS pairing pattern P is an 18 × 18 color-flavor-spin matrix qα

iaqβ jb1PI = ∆P Pαβ ij ab

The attractive channel is: color antisymmetric [most attractive] space symmetric [s-wave pairing] spin antisymmetric [isotropic] ⇒ flavor antisymmetric

Start with the most symmetric case, where all three flavors are massless.

Three massless quark flavors

Valid at very high density (µ ≫ ms) Color-flavor locked pairing pattern qα

i qβ j ∼ δα i δβ j − δα j δβ i = ǫαβnǫijn

color α, β flavor i, j

This is invariant under equal and opposite rotations of color and (vector) flavor SU(3)color × SU(3)L × SU(3)R

• ⊃ U(1)Q

×U(1)B → SU(3)C+L+R

• ⊃ U(1) ˜

Q

×Z2

◮ Breaks chiral symmetry, but not by a ¯

qq condensate

◮ Unbroken “rotated” electromagnetism: photon-gluon mixture ◮ Continuity between hadronic (hyperonic) and CFL phases ◮ Transparent insulator

(but see [ Windisch (Mon) ])

Conjectured QCD phase diagram

liq

T µ

gas

QGP CFL

nuclear /supercond superfluid

compact star

non−CFL

heavy ion collider

hadronic

• III. Quark matter in the real world

In the real world there are three factors that combine to oppose pairing between different flavors.

• 1. Strange quark mass is not infinite nor zero, but intermediate. It

depends on density, and ranges between about 500 MeV in the vacuum and about 100 MeV at high density.

• 2. Neutrality requirement.

Bulk quark matter must be neutral with respect to all gauge charges: color and electromagnetism.

• 3. Weak interaction equilibration.

In a compact star there is time for weak interactions to proceed: neutrinos escape and flavor is not conserved. These factors favor different Fermi momenta for different flavors which

• bstructs pairing between different flavors.

Mismatched Fermi surfaces vs. Cooper pairing

F

p d

F

p s

µ

E p

s and d quarks near their Fermi surfaces cannot have equal and

• pposite momenta.

The strange quark mass is the cause of the mismatch. pFd − pFs ≈ pFd − pFu ≈ M2

s

4µ

Phases of quark matter, again

liq

T µ

gas

QGP CFL

nuclear /supercond superfluid

compact star

non−CFL

heavy ion collider

hadronic

NJL model, uniform phases only

µB/3 (MeV) T (MeV) 550 500 450 400 350 60 50 40 30 20 10 g2SC NQ NQ 2SC uSC guSC → CFL ← gCFL CFL-K0 p2SC− → χSB t t t t

Warringa, hep-ph/0606063

But there are also non-uniform phases, such as the crystalline (“LOFF”/”FFLO”) phase. [ Incera (Mon) ]

• IV. Quark matter in neutron stars?

Conventional scenario Neutron/hybrid star

neutron star hybrid star NM NM

SQM

crust nuclear

Strange Matter Hypothesis

[ Mannarelli (Mon) ]

Strange star

crust strangelet

SQM SQM SQM

crust nuclear

Signatures of quark matter in compact stars

Observable ← Microphysical properties

(and neutron star structure) ← Phases of dense matter

Property Nuclear phase Quark phase mass, radius eqn of state ε(p) known up to ∼ nsat unknown; many models

Signatures of quark matter in compact stars

Observable ← Microphysical properties

(and neutron star structure) ← Phases of dense matter

Property Nuclear phase Quark phase mass, radius eqn of state ε(p) known up to ∼ nsat unknown; many models spindown (spin freq, age) bulk viscosity shear viscosity Depends on phase: n p e n p e, µ n p e, Λ, Σ− n superfluid p supercond π condensate K condensate Depends on phase: unpaired CFL CFL-K 0 2SC CSL LOFF 1SC . . . cooling (temp, age) heat capacity neutrino emissivity thermal cond. glitches (superfluid, crystal) shear modulus vortex pinning energy mergers (grav waves) eqn of state bulk viscosity

Probing the Equation of State

Assuming that General Relativity is correct [ Llanes-Estrada (Tues) ], Equation of State can be indirectly measured via its effect on mass-radius relation, and on gravitational and electromagnetic signals emitted in neutron star mergers [ Rezzolla (Tues) ][ Gorda (Tues) ]

◮ EoS may be very similar in different phases

(e.g. superfluid vs. “normal”).

◮ Transport properties are a better discriminator [ Stetina (Tues) ] ◮ Strongly first order phase transition is reflected in EoS,

(e.g. nuclear to quark matter?) How would a strong first-order transition in the EoS be manifest in mass-radius measurements?

CSS: EoS with generic first-order transition

Model-independent parameterization with

• Sharp 1st-order transition
• Constant [density-indp]

Speed of Sound (CSS) ε(p) = εtrans +∆ε+c−2

QM(p −ptrans)

ε0,QM εtrans ptrans cQM

• 2

Slope = Matter Quark Matter Nuclear

Δε

Energy Density Pressure

QM EoS params: ptrans/εtrans ∆ε/εtrans c2

QM

Zdunik, Haensel, arXiv:1211.1231; Alford, Han, Prakash, arXiv:1302.4732

Hybrid star M(R)

Hybrid star branch in M(R) relation has 4 typical forms ∆ε < ∆εcrit small energy density jump at phase transition

“Connected”

R M

“Both”

M R

∆ε > ∆εcrit large energy density jump at phase transition

“Absent”

R M

“Disconnected”

M R

“Phase diagram” of hybrid star M(R)

Soft NM + CSS(c2

QM =1)

6.0 5.0 3.0

ntrans/n0

B A

2.0 4.0

C

ncausal

D

Δε/εtrans = λ-1

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

Schematic

εtrans ∆ε ε

trans trans

p

Above the red line (∆ε > ∆εcrit), connected branch disappears ∆εcrit εtrans = 1 2 + 3 2 ptrans εtrans

Disconnected branch exists in regions D and B.

Constraints on QM EoS from Mmax

Alford, Han arXiv:1508.01261

2 M⊙ observation allows two scenarios:

• high ptrans: very small

connected branch

• low ptrans: modest ∆ε,

no disconnected branch. With c2

QM 1 3 it is difficult for any EoS to achieve a 2M⊙ star.

Neutron star mergers

Mergers probe the properties of nuclear/quark matter at high density (up to ∼ 4nsat) and temperature (up to ∼ 60 MeV)

−15 −10 −5 5 10 15

x [km]

−15 −10 −5 5 10 15

y [km]

t = 2.42 ms

12 13 14 15

log10(ρ [g/cm3])

Rezzolla group, Frankfurt Video

In developing signatures for quark matter, we must include all the relevant physics for nuclear matter.

Nuclear material in a neutron star merger

• M. Hanauske, Rezzolla group, Frankfurt

Significant spatial/temporal variation in: so we need to allow for temperature thermal conductivity fluid flow velocity shear viscosity density bulk viscosity

Role of transport in mergers

We can estimate the equilibration times for various forms

• f dissipation, to decide which is the most important.

(Alford, Bovard, Hanauske, Rezzolla, Schwenzer, arXiv:1707.09475) ◮ Thermal equilibration: If neutrinos are trapped, and there are

short-distance temperature gradients then thermal transport might be fast enough to play a role. τ (ν)

κ

≈ 700 ms ztyp 1 km

• 2

T 10 MeV

• 2 0.1

xp

• 1/3 m∗

n

0.8 mn

• 3 µe

2µν

• 2

◮ Shear viscosity: similar conclusion. ◮ Bulk viscosity:

If Direct Urca processes remain suppressed at the relevant densities and temperatures, bulk viscosity will quickly damp density oscillations τ min

ζ

≈ 3 ms tcomp 1 ms K 250 MeV 0.25 MeV Yζ

• V. Looking to the future

Critical/crossover density for nuclear→quark transition is unknown. Neutron stars may have quark matter cores. We need signatures that are sensitive to properties of the core

◮ Neutron stars:

◮ More data on neutron star mass, radius, age, temperature, etc. ◮ Understand mergers: role of EoS, bulk viscosity,. . . ◮ Spindown: understand r-mode damping and saturation

[ Andersson (Tues) ]

◮ Glitches: possible role of color supercond. crystalline phase?

◮ Quark matter properties:

◮ Intermediate density phases: crystalline? color-spin-locked? ◮ Better models of quark matter: Functional RG, Schwinger-Dyson ◮ Role of large magnetic fields [ Moreira (Wed) ] [ Schmitt (Tues) ] ◮ Solve the sign problem and do lattice QCD at high density

Extra slides

Nucl/Quark EoS ε(p) ⇒ Neutron star M(R)

7 8 9 10 11 12 13 14 15 Radius (km) 0.0 0.5 1.0 1.5 2.0 2.5 Mass (solar)

AP4 MS0 MS2 MS1 MPA1 ENG AP3 GM3 PAL6 GS1 PAL1 SQM1 SQM3 FSU GR P <

• c

a u s a l i t y rotation J1614-2230

J1903+0327 J1909-3744 Double NS Systems

Nucleons Nucleons+ExoticStrange Quark Matter

Heaviest known star: M = 2.01 ± 0.04 M⊙

Antoniadis et al, arXiv:1304.6875 Demorest et al, arXiv:1010.5788

Can quark matter be the favored phase at high density?

Sensitivity to Nuclear EoS and c2

QM c2

QM =1/3

B A

NL3

C

HLPS

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

c2

QM =1

B A

NL3

C

HLPS

D

Δε/εtrans

0.2 0.4 0.6 0.8 1 1.2

ptrans/εtrans

0.1 0.2 0.3 0.4 0.5

• Nuclear Matter EoS does not make much difference.

(HLPS is soft, NL3 is stiff)

• Higher c2

QM favors disconnected branch.

Low ptrans and high ptrans windows

Constraints on QM EoS from R1.4 M⊙

Low transition pressure and R1.4 M⊙

◮ R1.4 M⊙ contours roughly follow mass contours ◮ Mmax > 1.95 M⊙ requires R1.4 M⊙ > 12 km (ntrans ≈ n0), rising

with ntrans.

◮ dashed line is Mmax = 2.1 M⊙, requires R1.4 M⊙ > 12.7 km ◮ Observation of a smaller 1.4 M⊙ star ⇒ c2 QM > 1/3. ◮ If ptrans is high then no hybrid stars have mass 1.4 M⊙

compare Lattimer arXiv:1305.3510: R > 11 km.

Constraints on r-mode amplitude

• Αsat1010

Αsat105 Αsat1 106 107 108 109 1010 100 200 300 400 500 600 700

T K f Hz

steady-state lines (r-mode heating = mod. Urca cooling) for given r-mode amplitude αsat. LMXBs have accretion heating too ⇒ hotter than r-mode steady state. αsat 10−8 No known saturation mechanism can achieve this.

(Alford, Schwenzer, arXiv:1310.3524)